I'm pretty sure it needs to be sōlis: "by/with the light of the sun". I can't imagine why "lūce sōle" would make sense, because neither "lūx" nor "sōl" is an adjective, so there's no apparent way that one could be modifying the other.

You could possibly say "Lūna sōle illustrātur", though, in which case you see the sun as an instrument by which the moon is lighted.